The relationship between AR (Average Revenue), MR (Marginal Revenue), and Price Elasticity of Demand can be explained as follows:

a) MR = AR [e-1/e]: This equation suggests that the marginal revenue (MR) is equal to the average revenue (AR) multiplied by the price elasticity of demand (e) minus 1, divided by the price elasticity of demand (e). This relationship shows how changes in price elasticity affect the marginal revenue generated by each additional unit of output sold. If the price elasticity of demand is greater than 1 (e>1), MR will be positive, indicating that the firm can increase revenue by lowering prices. If the price elasticity of demand is less than 1 (e<1), mr="" will="" be="" negative,="" suggesting="" that="" the="" firm="" should="" increase="" prices="" to="" maximize="" revenue.="" when="" the="" price="" elasticity="" of="" demand="" equals="" 1="" (e="1)," mr="" will="" be="" zero,="" indicating="" that="" revenue="" is="" maximized="" at="" the="" current="" price="">

b) MR = AR: This equation states that the marginal revenue (MR) is equal to the average revenue (AR). In this case, the price elasticity of demand is not explicitly considered. This relationship suggests that the additional revenue generated by selling one more unit of output is the same as the average revenue obtained from all units sold. This occurs when the demand curve is perfectly elastic, implying that the firm can sell any quantity at the same price.

In summary, the relationship between AR, MR, and Price Elasticity of Demand can vary depending on the specific equation used. Equation a) incorporates the price elasticity of demand into the calculation of MR, allowing for a more nuanced understanding of how changes in elasticity impact revenue. Equation b) assumes that MR is equal to AR, without explicitly considering the price elasticity of demand.